Illustration of Optimal Levels of Multiple Inputs

A final look at the Tax Advisors, Inc., example illustrates these relations. Recall that with three CPAs and four bookkeepers, the ratio of marginal products to price for each input indicates a need to employ more CPAs relative to the number of bookkeepers. Assume that hiring one more bookkeeper leaves unchanged their marginal product of 0.3 tax returns processed per hour (MPB=5 = 0.3). In addition, assume that with this increased employment of bookkeepers the marginal product of the fourth CPA increases from 0.4 to 0.7 tax returns processed per hour. This assumption reflects the fact that the marginal productivity of an input factor (CPAs) is typically enhanced when used in conjunction with more of a complementary input, bookkeepers in this case. Now M^Pg-5 = 0.3 and ^MPcpa=4 =

0.7. With the costs of each input remaining constant at PB = $15 and PCPA = $35, the marginal product-to-price ratios are now equal:

= 0.02 Units per Dollar (for bookkeepers)

pcpa $35

= 0.02 Units per Dollar (for CPAs)

The combination of four CPAs and five bookkeepers is now optimal from a cost-minimizing standpoint, and input proportions are optimal. However, it is unclear whether an optimal level of input has been employed. Does the resulting output level maximize profit? To answer this question, it becomes necessary to determine if marginal revenue product equals the marginal cost of each input. If net marginal revenue (NMR) per return remains at $50 = ($100 X 0.5), then

MRPb = MPb X NMRq

Marginal revenue product equals marginal cost for each input. The combination of four CPAs and five bookkeepers is an optimal level of employment because the resulting output quantity maximizes profit.

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